In this talk I will talk about the Hamilton-Jacobi-Bellman equations with distribution-valued coefficients, which is not well-defined in the classical sense and shall be understood by using paracontrolled distribution method introduced in /cite{GIP15}. By a new characterization of weighted H/"older space and Zvonkin's transformation we prove some new a priori estimates, and therefore, establish the global well-posedness for singular HJB equations. As an application, the global well-posedness for KPZ equations on the real line in polynomial weighted H/"older spaces is obtained without using Cole-Hopf's transformation. This is based on the joint work with Xicheng Zhang and Xiangchan Zhu.

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